This project will develop a set of analytical models and measurement techniques that calibrate action sequences to specific aspects of social settings and cultural context. These methods will allow for the representation of social settings as "relational conjunctives," composed of complex interpretations of individuals, organizations, and discursive forms over time. Through a combination of algebraic and statistical techniques (k-partite lattices and random graph models), the research will explore the relationship between descriptive/exploratory and probabilistic/explanatory approaches to these sorts of interdependencies. The models to be used center on lattice and graph theoretic decomposition propositions, supplemented by Markov chain and random assignment algorithms.
The methodological tools developed through this project will contribute to our understanding of the sociocultural dynamics of social settings. The project will involve collaboration between U.S. and Australian research teams over a one-year period, during which a new set of formal mathematical techniques will be developed, refined, and applied to several substantive research projects. One data set will come from a two-year field study of management workgroups and networks in a major New York bank. A second data set comes from field study over a four-year period of political and social movement mobilization in Brazil. A third data set will be developed from a longitudinal sociometric and attitudinal study of friendship relations in a large Australian university. We also will explore the extrapolation of such models to theoretical and empirical studies of production markets. The possible applications of this approach can be extended to many other problems in historical, organizational, and sociolinguistic research. The resulting models and techniques represent a next wave in mathematical network analysis, by allowing us to explore the multi-dimensional and contingent nature of social processes as embedded in sociocultural network relations.
